Abstract

Changes in the radiance and state of polarization of a beam of radiation can often be described by means of a pure Mueller matrix. Such a 4 × 4 matrix transforms Stokes parameters and can be expressed in terms of the elements of a 2 × 2 Jones matrix. Relations between the two types of matrix are discussed. Explicit expressions are given for changes of a pure Mueller matrix that are caused by certain elementary changes of its Jones matrix, such as when its transpose, complex conjugate, or Hermitian conjugate are taken. It is shown that every pure Mueller matrix has a simple and elegant structure, which is embodied by interrelations that involve either only squares of the elements or only products of different elements. All possible interrelations for the elements of a general pure Mueller matrix are derived from this simple structure.

Figures (1)

The 16 dots in each pictogram represent the elements of a pure Mueller matrix. A solid line or curve connecting two elements represents a positive product, and a dashed curve or line represents a negative product. In each pictogram, the sum of all positive and negative products vanishes. (a) Twelve pictograms that represent equations that carry corresponding products of any two chosen rows and columns. (b) Eighteen pictograms that demonstrate that the sum or difference of any chosen pair of complementary subdeterminants vanishes.